A general model for the spread of an epidemic with S as the proportion of the po

Question

A general model for the spread of an epidemic with S as the proportion of the population that is susceptible, I as the proportion of the population that is infected, and R as the proportion of the population that is recovered can be modeled as the following set of differential equations: dS/dt=r(I-S)-bSI dI/dt=bSI-cI dR/dt=cI. Whether the recovered proportion becomes susceptible or not depends on the disease, but in either case they can be factored in without explicit description by adjusting r so we can concentrate on just the first two equations for our analysis. a. Explain what the parameters r, b and c are in the model. b. Using just the first two equations, find the two relevant equilibrium points. What has to be true about the parameters for two relevant equilibrium points to exist? c. Sketch the nullclines for this system along with directions. d. Conduct a linearized analysis for this system and discuss the stability of the two equilibrium points. What has to be true about the parameter so that there is a locally stable equlibrium point.

Explanation / Answer

(A)here r is the population proportion and b and c are constants

(B)ds/dt=r(l-s)-bsl

dl/dt=bsl-cl

here is two quilibrim points are occur l,s

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